Open-channel flow (Manning) worksheet with answers

Free printable Open-channel flow (Manning) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
b = 3.5 my = 1.5 mn = 0.015

Water flows uniformly 1.5 m deep in a rectangular brickwork channel 3.5 m wide (Manning n = 0.015). The bed slope is S = 0.004. Use Manning’s equation in SI units to find the mean velocity V.

b = 3.5 my = 1.5 mn = 0.015S = 0.004
V = m/s
2.Easy
b = 2 my = 1 mn = 0.015

Water flows uniformly 1 m deep in a rectangular brickwork channel 2 m wide (Manning n = 0.015). The bed drops 5 m per kilometre. Use Manning’s equation in SI units to find the mean velocity V.

b = 2 my = 1 mn = 0.015drop = 5 m/km
V = m/s
3.Medium
b = 5.5 my = 2.4 mn = 0.015, S = 0.0015

A rectangular brickwork channel is 5.5 m wide. Water flows uniformly 2.4 m deep. Manning n = 0.015 and the bed slope is S = 0.0015. Find the flow rate Q in m³/s.

b = 5.5 my = 2.4 mn = 0.015S = 0.0015
Q = m³/s
4.Medium
D = 900 mmn = 0.013, S = 0.0008

A concrete storm sewer with an inside diameter of 900 mm flows just full (as an open channel, not under pressure). Manning n = 0.013 and the slope is S = 0.0008. Find the flow rate Q in m³/s.

D = 900 mmn = 0.013S = 0.0008
Q = m³/s
5.Hard
b = 3.5 my = 0.9 m1 : 1n = 0.015, Q = 14 m³/s

A trapezoidal brickwork channel with a bottom width of 3.5 m and side slopes of 1:1 (horizontal:vertical) must carry 14 m³/s in uniform flow at a depth of 0.9 m. Manning n = 0.015. Find the required bed slope S (in m/m).

Q = 14 m³/sb = 3.5 my = 0.9 mz = 1n = 0.015
S = m/m
6.Hard
D = 600 mmn = 0.013, V = 1 m/s

A concrete sewer with an inside diameter of 600 mm (Manning n = 0.013) must reach a self-cleansing velocity of 1 m/s when flowing just full. Find the minimum slope S (in m/m).

D = 600 mmn = 0.013V = 1 m/s
S = m/m

Answer key

  1. 1. V = 3.657 m/s
  2. 2. V = 2.97 m/s
  3. 3. Q = 40.21 m³/s
  4. 4. Q = 0.512 m³/s
  5. 5. S = 0.004944 m/m
  6. 6. S = 0.00212 m/m

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